The present invention relates to a system for multiresolutional analysis of a complex system which cannot be adequately described with a mathematical model, and more particularly, to a method of multiresolutional analysis for optimizing the performance of an industrial facility, system and/or device which do not have an adequate model of representation.
Human beings accomplish tasks by developing an organized hierarchical structuring of information which "lumps" information at various levels of "resolution" (granularity, and/or scale). The information is then retrieved and employed at the appropriate resolution level. Information collected at a more general, or overview level is generally considered to be less precise, but more easily retained and retrieved. Such data is said to be low resolution level. Information collected at a detailed level is typically more precise, but is more difficult to retain and retrieve because of its abundance. Also it increases the complexity of computation to a prohibitively high level. Such detailed information is generally termed high resolution level data. The complexity of computations at this level can be bounded by reducing the scope of the represented space of interest. When an individual acts on a task, the normal process is to constrain detailed action (higher resolution activity) based on general information (lower resolution data). A process of selecting "good" versus "bad" data is employed to make decisions.
Simulation and modeling systems use mathematical models to fully describe systems or activities. The difference between the human approach and a computer-simulated approach is that the human mind does not rely on such mathematical models. The concept and application of different resolution levels to automation and control systems is normally referred to as "supervisory control" and has been used in limited applications where the lower resolution system is only one or two levels above the higher resolution system. One such example is a unit load control system in a power plant. In such a system, the required megawatt (MW) output demand is defined at an overview level for the system. The demand value is then used in constraining functions to control subsystems (e.g., fuel/air, feed water, turbine valves) such that the megawatt demand is met. The operation of a power generating station highlights the semiotic relationships of dependent and independent process variables at multiple, discrete levels of resolution.
Generally, planning and control systems include a specified goal according to some cost or other criterion. The classical approach to designing a control system generally comprises three stages: (1) develop or identify a model of the process or operation to be controlled, (2) validate the model using a known range of operating conditions, and (3) select optimal input values to achieve a desired system behavior. The first stage, development of a model, involves the selection of an appropriate mathematical structure for purposes of identification. The mathematical structure represents a class of models which may be used to reproduce the input-output relationship of the system to be controlled. The semiotic character of the relationships in this case is taken care of by the symbol grounding procedures which employ on-line or pretabulated operations of interpretation. The mathematical structure is associated with a set of parameters, .THETA., so that the class of models may be represented in symbolic form as M(.THETA.). The identification problem involves determining the parameter set such that the difference between an observed and predicted input-output behavior of the target system is minimized across the class of models. The second, validation stage may be performed concurrently with identification. The role of the validation stage is to verify the fidelity of the model across the expected range of operating conditions for the target system. In a system with an analytical model, validation is of deep concern because, in reality, the models are valid only for a limited time period, and in large complex systems, the limited time period is very small. The final stage is behavior generation, where having synthesized an adequate mathematical model, the selection of optimal input-output behavior is attempted using one of several existing analytical techniques. The latter are usually associated with well-known techniques (such as dynamic programming and/or maximum principle) however all of them dwell upon search algorithms and are very costly computationally. In order to provide for the input-output behavior, input-output maps are computed and a second set of maps is generated for error compensation. When this approach is applied on-line, it is called control; when this approach is applied off-line, it is called planning. The latter is used to compute feedback control strings so that the on-line control (feedback compensation) can be done only to compensate for deviations from a feed-forward generated planned trajectory.
In the classical approach, several implicit assumptions are made in order to simplify the required analysis. The most common and significant of the assumptions is that the class of models may be chosen from a set of smooth differential equations of the type: EQU y(t)+a.sub.1 y.sup.(n -1) (t)+a.sub.2 y.sup.(n-2) (t)+. . . +a.sub.n y(t)=b.sub.1 u.sup.(n-1) (t)+b.sub.2 u.sup.(n-2) (t)+. . . +b.sub.n u(t)
for which the parameter set could be written as .THETA.=(a.sub.1, a.sub.2, . . . , a.sub.n, b.sub.1, b.sub.2, . . . , b.sub.n). A more general formulation of the class of mathematical structures might be closer to EQU x(t)=Ax(t)+Bu(t)+V(t)+N(x,u,t) EQU y(t)=Cx(t)+W(t)+M(x,u,t)
where the A, B, and C matrices are coefficients of terms linear in state and input, V and W are noise terms, and N and M are non-linear components of the model. Further, generality could be obtained by including partial derivatives in the formulation.
The use of a class of candidate models which is capable of representing stochastic and non-linear dynamics which contribute significantly to system behavior in many settings, raises the complexity of behavior generation and optimization strategies. The difficulties grow substantially when both input-output pairs, as well as the parameter set are subject to disturbances. The problem becomes very difficult to solve when the system demonstrates distributed character. Existing analytical techniques are not suited to mathematical models in this form. Consequently, superior identification techniques are of little value unless methods of behavior generation and optimization are utilized which can determine useful strategies for this class of models. The classical approach is especially difficult to apply when trying to control a large complex system. Mathematical models for such systems are not well known and often are erroneous, so that the results of computations are fuzzy.
The present invention is directed to a process control system which determines optimal trajectories (input controls) using multiresolutional analysis of acquired data. In contrast to prior art control systems, the present invention does not use a predetermined mathematical model or algorithm which defines the process in terms of a plurality of variables. Rather, the present invention acquires system data and stores the data in a multiresolutional data structure. A knowledge base is thus created, which is searched at varying levels of resolution for determining optimal process trajectories. This base can be called "a model" in a very general sense. It is rather a fluid "provisional data structure" which is created and recreated on demand, to support the decision making process. The continual addition of data to the data structure allows for continual refinement of the determined trajectories.